Question

A block weighing 7.2 N requires a force of 3.1 N to push it along at constant velocity. What is the coefficient of friction for the surface? part 2 of 2 A weight W is now placed on the block and 7.2 N is needed to push them both at constant velocity. What is the weight W of the block? Answer in units of N. Answer in units of N

Answer 1

The coefficient of friction for the surface is calculated using the normal force and the applied force needed to move the block at a constant velocity, which results in μ being 3.1 N divided by 7.2 N. For the additional weight, the same coefficient is used to find the weight added to the block by solving a proportion.

Step-by-step explanation:

To find the coefficient of friction for the surface, we use the equation for frictional force (f) which is the product of the normal force (N) and the coefficient of friction (μ). The force of friction can be calculated using the force necessary to move the block at a constant velocity, which is 3.1 N. Since the block weighs 7.2 N, the normal force (N) is equal to the weight, and thus 7.2 N as well due to the block being on a horizontal surface and assuming no other vertical forces. Therefore, the coefficient of friction is μ = f / N = 3.1 N / 7.2 N.

For the second part, if a weight (W) is added to the block and 7.2 N is again needed to push both at constant velocity, the normal force is now the weight of the block plus the additional weight (W). As the force necessary to move the block at constant velocity with the additional weight remains the same, the coefficient of friction and thus the ratio f / N is also the same. By setting up a proportion, we can solve for the new normal force, 3.1 N / 7.2 N = 7.2 N / (7.2 N + W), and find the value of W.

Answer 2

The coefficient of friction for the surface is approximately 0.4306, and when an extra weight is added to the block, the required force to push them remains unchanged at 7.2 N, which implies that the weight of the added block is 0 N.

Step-by-step explanation:

The coefficient of friction can be determined using the relationship between the frictional force and the normal force. Based on Newton's second law, if a block is moving at a constant velocity on a horizontal surface, the net force acting on the block is zero. This means that the applied force to move the block is balanced by the frictional force. As given, a force of 3.1 N is required to move the initial 7.2 N block at constant velocity, implying that the frictional force is 3.1 N.

The coefficient of friction (μ) is calculated as the ratio of the frictional force (f) to the normal force (N). In this case, μ = f / N = 3.1 N / 7.2 N = 0.4306.

When an additional weight (W) is added, and the total force needed to move the block at constant velocity is still 7.2 N, this indicates that the total weight of both the block and the additional weight is balanced by the normal force. The frictional force is equal to the coefficient of friction times the normal force, which we can write as f = μN = 7.2 N. However, since 7.2 N was also the weight of the block without the additional weight, the additional weight W adds no net force; thus, W must be zero Newtons.