Middle School

A 20 kg box is being pulled across a floor by a horizontal rope. The tension in the rope is 99 Newtons, and the coefficient of friction is 0.25.

1. What is the force of friction on the box?
2. What is the acceleration of the box?

Answer :

Final answer:

The force of friction on the 20 kg box is 49 N, and the acceleration of the box is 2.5 m/s². These were calculated using the formulas for the force of friction (F=μN) and acceleration (F=ma), along with given information on tension, friction coefficient, and mass.

Explanation:

The force exerted by friction, also known as the force of friction, can be found using the formula F = μN, where μ is the coefficient of friction and N is the normal or perpendicular force (which is 20 kg * 9.8 m/s² = 196 N as gravity is 9.8 m/s²). Therefore, the force of friction is 0.25 * 196 N = 49 N.

Now, we will figure out the acceleration of the box. According to Newton's second law of motion, which is F = ma, the net force is equal to the mass times the acceleration. The net force here is the difference between the tension force and the friction force (99 N - 49 N = 50 N). So, to find acceleration, we will divide the net force by the mass. Thus, acceleration = 50 N / 20 kg = 2.5 m/s².

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