Question

In Fig. 4.15 an astronaut is playing shuffleboard on Earth. The puck has a mass of \(2.0 \mathrm{kg} .\) Between the board and puck the coefficient of static friction is 0.35 and of kinetic friction is \(0.25 .\) (a) If she pushes the puck with a force of \(5.0 \mathrm{N}\) in the forward direction, does the puck move? (b) As she is pushing, she trips and the force in the forward direction suddenly becomes \(7.5 \mathrm{N} .\) Does the puck move? (c) If so, what is the acceleration of the puck along the board if she maintains contact between puck and stick as she regains her footing while pushing steadily with a force of \(6.0 \mathrm{N}\) on the puck? (d) She carries her game to the Moon and again pushes a moving puck with a force of \(6.0 \mathrm{N}\) forward. Is the acceleration of the puck during contact more, the same, or less than on Earth? Explain. (tutorial: rough table)

Short answer

Answer: Compare the applied forces (5.0 N and 7.5 N) with the static friction force on Earth to determine if the puck moves. Calculate the acceleration on Earth when a 6.0 N force is applied by using Newton's second law and considering the net force (the applied force minus the kinetic friction force). Then, repeat these steps for the Moon using its gravitational acceleration (1.63 m/s^2) and compare the acceleration values for both cases.

Step-by-step solution

Calculate static friction force

First, calculate the static friction force (\(f_s\)) using the formula: \(f_s = \mu_s F_N\) where \(\mu_s\) is the static friction coefficient, and \(F_N\) is the normal force. Since the puck is on a horizontal surface, \(F_N = mg\) where \(m\) is the mass of the puck, and \(g\) is the acceleration due to gravity (9.8 m/s^2 for Earth). So, \(f_s = \mu_s mg\).

Calculate kinetic friction force

Calculate the kinetic friction force (\(f_k\)) using the formula: \(f_k = \mu_k F_N\) where \(\mu_k\) is the kinetic friction coefficient. As in Step 1, the normal force is equal to \(mg\), so \(f_k = \mu_k mg\).

Determine if the puck moves at 5.0 N force

Compare the applied force (5.0 N) with the static friction force. If the applied force is greater than the static friction force, the puck will move. If not, it will stay stationary.

Determine if the puck moves at 7.5 N force

As in Step 3, compare the applied force (7.5 N) with the static friction force. If the applied force is greater than the static friction force, the puck will move. If not, it will stay stationary.

Calculate the puck's acceleration at 6.0 N force

If the puck is moving, use Newton's second law, \(F = ma\), to calculate the acceleration. First, find the net force acting on the puck, which is the difference between the applied force (6.0 N) and the kinetic friction force. Then, use the net force and the mass of the puck to calculate the acceleration.

Compare the acceleration on Earth and Moon

On the Moon, the only difference is the acceleration due to gravity, which is approximately 1/6 that of Earth. Since the normal force depends on the gravitational force, the frictional forces will also change. Repeat steps 1-5 for the Moon, with the Moon's gravitational acceleration (\(g_{moon} \approx 1.63 \, m/s^2\)). Compare the acceleration values for both cases to determine whether the acceleration is greater, the same, or less on the Moon.