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A boxed 10.0-kg computer monitor is dragged by friction 5.50 m upward along a conveyor belt inclined at an angle of 36.9 above the horizontal. If the monitor's speed is a constant 2.10 cm/s, how much work is done on the monitor by (a) friction, (b) gravity, and (c) the normal force of the conveyor belt?

Short Answer

Expert verified
Work by gravity: -3.3 kJ; by normal force: 0; friction typically adapts to zero net work.

Step by step solution

01

Identify the forces involved

The problem involves three main forces acting on the monitor: friction, gravity, and the normal force. We need to calculate the work done by each force as the monitor is dragged along the conveyor belt.
02

Calculate the work done by friction

The force due to friction (Ffriction ) can be calculated from the work-energy principle. Since the velocity is constant, net work is zero. The work done by friction, Wfriction, is equal to the force of friction times the displacement d times cos(θ), where θ=180 because friction opposes the motion: Wfriction=Ffrictiondcos(180)=Ffriction5.5.To solve for Ffriction, we need additional information like the coefficient of friction; hence, typically it's derived from balance with other forces in practical scenarios.
03

Calculate the work done by gravity

The gravitational force acting on the monitor is Fgravity=mg=10.09.8. The work done by gravity is calculated by: Wgravity=Fgravitydcos(ϕ),where ϕ=36.9+90=126.9. Thus, Wgravity=10×9.8×5.5×cos(126.9).Calculate to find the negative work done by gravity as it is acting downward.
04

Calculate the work done by the normal force

The normal force acts perpendicular to the direction of displacement, hence the angle between the direction of the normal force and the motion is 90. Therefore, the work done by the normal force is:Wnormal=Fnormaldcos(90)=0.
05

Calculate numerical values

1. Compute the gravitational work: Wgravity=10×9.8×5.5×cos(126.9)=10.0×9.8×5.5×(0.6)=3.3kJ.2. Work by normal force is already determined as 0.3. Work by friction is typically calculated to complement the zero net work in this situation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Inclined Plane Problems
When dealing with inclined plane problems in physics, we often encounter scenarios where objects are moved along a slope or an incline. This exercise showcases such a problem, where we focus on a boxed monitor on a conveyor belt inclined at 36.9 degrees. The angle of the incline significantly impacts the forces acting on the object. Understanding how to break down these forces into components along the plane and perpendicular to it is key to solving these problems.

Key things to consider for inclined plane problems include:
  • Identifying the incline angle: This affects the gravitational force component along the plane.
  • Analyzing forces: Typically involve gravity, the normal force, and friction.
  • Calculating displacement parallel to the incline, which helps determine work done by various forces.
For successful problem-solving, one should focus on decomposing forces into parallel and perpendicular components relative to the plane. This aids in calculating work done by each force more straightforwardly.
Frictional Force Calculations
Frictional force calculations are crucial in determining how much resistance an object encounters while moving along a surface. In this exercise, friction plays an important role as it opposes the motion of the monitor. The frictional force typically requires the coefficient of friction, which was not explicitly given, indicating the need for further context or information from experiments or balance equations.

Points to remember when calculating frictional forces include:
  • Friction opposes motion, thus the work done is generally negative.
  • Net work is zero when speed is constant, meaning frictional and other forces balance out.
  • The work-energy principle can assist in identifying frictional forces by aligning with known energy changes.
Understanding these elements can help approach frictional calculations methodically, ensuring that forces such as friction are thoroughly accounted for in physics problems involving movement along inclined planes.
Gravitational Work
Gravitational work refers to the work done by gravitational force when an object moves along a particular path. In this scenario, the gravitational force is continuously acting downwards while the monitor is dragged upwards on the inclined conveyor belt.

Consider the following when calculating gravitational work:
  • The gravitational force (Fgravity=mg) depends on the mass and gravitational acceleration.
  • The angle affects the cosine component in the work equation, wherecos(126.9) indicates the direction opposing movement.
  • Negative work illustrates gravity acting against the upward motion.
Using the correct angle references and understanding the impact of gravity in different motion scenarios, you can effectively compute the gravitational work in similar inclined plane problems. The correct interpretation of direction and angles is vital in minimizing errors in these calculations.

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Most popular questions from this chapter

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. When you push the platform, you compress the springs. You do 80.0 J of work when you compress the springs 0.200 m from their uncompressed length. (a) What magnitude of force must you apply to hold the platform in this position? (b) How much additional work must you do to move the platform 0.200 m farther, and what maximum force must you apply?

Use the workenergy theorem to solve each of these problems. You can use Newton's laws to check your answers. (a) A skier moving at 5.00 m/s encounters a long, rough horizontal patch of snow having a coefficient of kinetic friction of 0.220 with her skis. How far does she travel on this patch before stopping? (b) Suppose the rough patch in part (a) was only 2.90 m long. How fast would the skier be moving when she reached the end of the patch? (c) At the base of a frictionless icy hill that rises at 25.0 above the horizontal, a toboggan has a speed of 12.0 m/s toward the hill. How high vertically above the base will it go before stopping?

We usually ignore the kinetic energy of the moving coils of a spring, but let's try to get a reasonable approximation to this. Consider a spring of mass M, equilibrium length L0, and force constant k. The work done to stretch or compress the spring by a distance L is \(\frac{1}{2}\) kX2, where X=LL0. Consider a spring, as described above, that has one end fixed and the other end moving with speed v. Assume that the speed of points along the length of the spring varies linearly with distance l from the fixed end. Assume also that the mass M of the spring is distributed uniformly along the length of the spring. (a) Calculate the kinetic energy of the spring in terms of M and v. (Hint: Divide the spring into pieces of length dl; find the speed of each piece in terms of l, v, and L; find the mass of each piece in terms of dl, M, and L; and integrate from 0 to L. The result is not \(\frac{1}{2}\) Mv2, since not all of the spring moves with the same speed.) In a spring gun, a spring of mass 0.243 kg and force constant 3200 N/m is compressed 2.50 cm from its unstretched length. When the trigger is pulled, the spring pushes horizontally on a 0.053-kg ball. The work done by friction is negligible. Calculate the ball's speed when the spring reaches its uncompressed length (b) ignoring the mass of the spring and (c) including, using the results of part (a), the mass of the spring. (d) In part (c), what is the final kinetic energy of the ball and of the spring?

The human heart is a powerful and extremely reliable pump. Each day it takes in and discharges about 7500 L of blood. Assume that the work done by the heart is equal to the work required to lift this amount of blood a height equal to that of the average American woman (1.63 m). The density (mass per unit volume) of blood is 1.05×103kg/m3. (a) How much work does the heart do in a day? (b) What is the heart's power output in watts?

Based on the given data, how does the energy used in biking 1 km compare with that used in walking 1 km? Biking takes (a) \(\frac{1}{3}\) of the energy of walking the same distance; (b) the same energy as walking the same distance; (c) 3 times the energy of walking the same distance; (d) 9 times the energy of walking the same distance.

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