Bob is pushing a box across the floor at a constant speed of 1.5 m/s, applying a horizontal force whose magnitude is 75 N. Alice is pushing an identical box across the floor at a constant speed of 3 m/s, applying a horizontal force.
(a) What is the magnitude of the force that Alice is applying to the box?
75N
To determine the magnitude of the force that Alice is applying to the box, we can use the formula:
Force = Mass × Acceleration
Since both boxes are identical, they have the same mass. Therefore, we can assume that the mass cancels out from the equation.
Given:
Bob's speed = 1.5 m/s
Bob's force = 75 N
Alice's speed = 3 m/s
We know that both boxes are moving at a constant speed, which means the net force acting on them is zero. In other words, the force applied by Alice must be equal in magnitude but opposite in direction to the friction force acting on the box. This friction force balances out the force applied by Alice to maintain a constant speed.
Therefore, we can set up the equation:
Force by Alice - Friction force = 0
We know that the friction force can be calculated using the equation:
Friction force = coefficient of friction × Normal force
Since both boxes are identical, their coefficients of friction and normal forces are the same. Therefore, the friction force on both boxes will also be the same.
Hence, the magnitude of the force that Alice is applying to the box is also 75 N.
To find the magnitude of the force that Alice is applying to the box, we can use the formula:
Force = mass * acceleration
Since both Bob and Alice are pushing identical boxes with the same constant speed, we can assume that the mass of the boxes is the same. Therefore, the force is directly proportional to the acceleration.
We know that Bob is applying a horizontal force of 75 N, which is causing the box to move at a constant speed of 1.5 m/s. Therefore, the acceleration of Bob's box is zero because the velocity is constant.
Since Alice's box is moving at a constant speed of 3 m/s, we can conclude that the acceleration of Alice's box is also zero. This means that the net force acting on the box is zero. So, the force that Alice is applying to the box must be equal in magnitude and opposite in direction to the force of friction acting on the box to keep it moving at a constant speed.
Therefore, the magnitude of the force that Alice is applying to the box is also 75 N.