Problem 1
Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 60.0\(^\circ\). If Rover exerts a force of 270 N and Fido exerts a force of 300 N, find the magnitude of the resultant force and the angle it makes with Rover's rope.
Problem 5
Forces \(\vec{F_1}\) and \(\vec{F_2}\)act at a point. The magnitude of \(\vec{F_1}\) is 9.00 N, and its direction is 60.0\(^\circ\) above the \(x\)-axis in the second quadrant. The magnitude of \(\vec{F_2}\) is 6.00 N, and its direction is 53.1\(^\circ\) below the \(x\)-axis in the third quadrant. (a) What are the \(x\)- and \(y\)-components of the resultant force? (b) What is the magnitude of the resultant force?
Problem 6
An electron (mass = 9.11 \(\times\) 10\(^{-31}\) kg) leaves one end of a TV picture tube with zero initial speed and travels in a straight line to the accelerating grid, which is 1.80 cm away. It reaches the grid with a speed of 3.00 \(\times\) 10\(^6\) m/s. If the accelerating force is constant, compute (a) the acceleration; (b) the time to reach the grid; and (c) the net force, in newtons. Ignore the gravitational force on the electron.
Problem 7
A 68.5-kg skater moving initially at 2.40 m/s on rough horizontal ice comes to rest uniformly in 3.52 s due to friction from the ice. What force does friction exert on the skater?
Problem 8
You walk into an elevator, step onto a scale, and push the "up" button. You recall that your normal weight is 625 N. Draw a free-body diagram. (a) When the elevator has an upward acceleration of magnitude 2.50 m/s\(^2\), what does the scale read? (b) If you hold a 3.85-kg package by a light vertical string, what will be the tension in this string when the elevator accelerates as in part (a)?
Problem 9
A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude 48.0 N to the box and produces an acceleration of magnitude 2.20 m/s\(^2\), what is the mass of the box?
Problem 10
A dockworker applies a constant horizontal force of 80.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 11.0 m in 5.00 s. (a) What is the mass of the block of ice? (b) If the worker stops pushing at the end of 5.00 s, how far does the block move in the next 5.00 s?
Problem 11
A hockey puck with mass 0.160 kg is at rest at the origin (\(x =\) 0) on the horizontal, frictionless surface of the rink. At time \(t =\) 0 a player applies a force of 0.250 N to the puck, parallel to the \(x\)-axis; she continues to apply this force until \(t =\) 2.00 s. (a) What are the position and speed of the puck at \(t =\) 2.00 s? (b) If the same force is again applied at \(t =\) 5.00 s, what are the position and speed of the puck at \(t =\) 7.00 s?
Problem 12
A crate with mass 32.5 kg initially at rest on a warehouse floor is acted on by a net horizontal force of 14.0 N. (a) What acceleration is produced? (b) How far does the crate travel in 10.0 s? (c) What is its speed at the end of 10.0 s?
Problem 15
A small 8.00-kg rocket burns fuel that exerts a timevarying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation \(F = A + Bt^2\). Measurements show that at \(t\) = 0, the force is 100.0 N, and at the end of the first 2.00 s, it is 150.0 N. (a) Find the constants \(A\) and \(B\), including their SI units. (b) Find the \(net\) force on this rocket and its acceleration (i) the instant after the fuel ignites and (ii) 3.00 s after the fuel ignites. (c) Suppose that you were using this rocket in outer space, far from all gravity. What would its acceleration be 3.00 s after fuel ignition?
