Question

A small motor runs a lift that raises a load of bricks weighing 836 N to a height of 10.7 m in 23.2 s. Assuming that the bricks are lifted with constant speed, what is the minimum power the motor must produce?

Short answer

The motor must produce a minimum power of approximately 385.6 watts.

Step-by-step solution

Understand the Problem

We need to find the power required to lift a load of bricks weighing 836 N to a height of 10.7 m in 23.2 seconds.

Calculate Work Done

The work done is given by the formula: \( Work = Force \times Distance \). Here, \( Force = 836 \ N \) and \( Distance = 10.7 \ m \). So, \( Work = 836 \ N \times 10.7 \ m = 8945.2 \ J \) (Joules).

Calculate Power

Power is the rate of doing work. The formula to calculate power is \( Power = \frac{Work}{Time} \). We calculated the work to be 8945.2 J and the time is 23.2 seconds. Therefore, \( Power = \frac{8945.2 \ J}{23.2 \ s} \approx 385.6 \ W \) (Watts).

Conclude

The minimum power that the motor must produce is approximately 385.6 watts.

Key concepts

Work-Energy Principle

The Work-Energy Principle is a fundamental concept in physics that explains how work and energy are related. When work is done on an object, energy is transferred to or from that object. This principle is vital in understanding how mechanical devices, like motors, operate. In our exercise example, work is being done by the motor on the bricks to move them upwards. The work done increases the bricks' potential energy as they gain height, exactly corresponding to the energy input, assuming no energy loss elsewhere due to, for instance, friction.
This relationship helps us understand why the calculation in the problem directly translates physical exertion into energy terms.

• Work quantifies the energy transferred to or from an object via force.
• This principle connects force, energy, and motion, making it easier to calculate energy changes.

Understanding this concept is crucial not just for our example but for analyzing any situation where forces move objects, resulting in energy transformation.

Constant Speed

The term "constant speed" describes a scenario where an object's motion remains uniform without acceleration. In the case of the bricks being lifted by the motor, moving at constant speed means there is no net change in the velocity of the bricks. This simplification implies that the force exerted by the motor is only equal to and offsets the weight of the bricks, removing any need to consider additional forces like friction or air resistance prominently in our calculations.

• Constant speed means that kinetic energy doesn't increase or decrease, simplifying power calculations.
• It allows us to focus purely on the gravitational forces and work done against gravity.

By lifting at a constant speed, the motor effectively transforms all its power output into moving the bricks vertically without wasting energy on changing speeds.

Mechanical Work

Mechanical work in physics refers to the quantity of energy transferred by a force acting through a distance. In our lifting exercise, the force the motor exerts on the bricks is up against gravity, calculated as the weight of the bricks, which is given.To find the work done, we multiply the force (weight of the bricks) by the distance over which the force is applied (the height).The formula used is: \[ Work = Force \times Distance \] For the exercise problem, this calculation yields a work of 8945.2 Joules (J).

• Work helps quantify the task the motor performs.
• It converts force and movement into an energy value, making physics problems solvable.

Mechanical work is a key factor in many practical applications, explaining how machines exert effort to cause movement or lift objects.

Joules and Watts

Joules and watts are units to measure energy and power respectively, and they are central to solving physics problems involving work and power. A joule (J) is the standard unit of energy or work in the International System of Units (SI). It represents the energy transferred when a force of one newton moves an object one meter.
A watt (W), on the other hand, is the unit of power, and it equates to one joule per second. When we calculated the power requirement of the motor, we used these units:

• The total work done, 8945.2 J, was divided by the time, 23.2 s, to calculate power, resulting in about 385.6 W.
• Watts enable us to understand how much work is done per second, linking practical applications to theoretical physics.

Mastering joules and watts helps us make sense of how energy is used and conserved in processes involving forces, such as the motor raising bricks.