Question

Two blocks are arranged at the ends of a massless string as shown in the figure. The

system starts from rest. When the 3.09 kg mass has fallen through 0.442 m, its downward speed is 1.35 m/s. The acceleration of gravity is 9.8 ms².
What is the frictional force between the 4.54 kg mass and the table? Answer in units of N.

Answer 1

The frictional force is found by calculating the work done by gravity and friction and equating it to the change in kinetic energy. The detailed calculation results in a frictional force of approximately 24.63 N.

The work done by gravity is given by the change in potential energy, which is the mass (3.09 kg) multiplied by the acceleration due to gravity (9.8 m/s²) multiplied by the height (0.442 m). Therefore, the work done by gravity is:

Work_gravity = 3.09 kg * 9.8 m/s² * 0.442 m

Work_gravity = 13.458 J

Now, the work done by friction is given by the frictional force (f_friction) multiplied by the distance (0.442 m). We are trying to find f_friction, so the work done by friction is:

Work_friction = f_friction * 0.442 m

According to the work-energy principle, the net work done is equal to the change in kinetic energy. The change in kinetic energy is given by:

ΔKE = 1/2 * mass * velocity²

Substitute the given values:

ΔKE = 1/2 * 3.09 kg * (1.35 m/s)²

ΔKE = 2.585 J

Now, equate the net work done to the change in kinetic energy:

Work_gravity - Work_friction = ΔKE

13.458 J - f_friction * 0.442 m = 2.585 J

Solve for f_friction:

f_friction * 0.442 m = 13.458 J - 2.585 J

f_friction * 0.442 m = 10.873 J

f_friction = 10.873 J / 0.442 m

f_friction = 24.63 N

Therefore, the frictional force between the 4.54 kg mass and the table is approximately 24.63 N.