A 10kg block rest on top of a 50kg block. A force of 120n is being pushed on the 10kg block at an angle of 45 deg. What is the magnitude of frictional force between the blocks? The cofficient is force is .4
To find the magnitude of the frictional force between the blocks, we need to determine the normal force and then use it to calculate the frictional force.
Step 1: Determine the normal force:
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of the top block.
Weight = mass * acceleration due to gravity
Weight of the 10kg block = 10kg * 9.8m/s^2 = 98N
So, the normal force exerted on the 10kg block is 98N.
Step 2: Calculate the frictional force:
The frictional force can be calculated using the equation:
Frictional force = coefficient of friction * normal force
Given that the coefficient of friction is 0.4 and the normal force is 98N, we can now calculate the frictional force.
Frictional force = 0.4 * 98N = 39.2N
Therefore, the magnitude of the frictional force between the blocks is 39.2N.
To solve this problem, we can follow these steps:
Step 1: Break down the force applied on the 10kg block into its horizontal and vertical components.
- The horizontal component of the force is given by F_horizontal = F_applied * cos(angle).
- F_horizontal = 120N * cos(45°)
- F_horizontal = 120N * √2/2
- F_horizontal = 84.85N
- The vertical component of the force is given by F_vertical = F_applied * sin(angle).
- F_vertical = 120N * sin(45°)
- F_vertical = 120N * √2/2
- F_vertical = 84.85N
Step 2: Calculate the normal force between the blocks.
- The normal force (N) is equal to the weight of the upper block (10kg) plus the weight of the lower block (50kg).
- N = (mass_upper_block + mass_lower_block) * g
- N = (10kg + 50kg) * 9.8m/s^2
- N = 588N
Step 3: Calculate the maximum possible frictional force.
- The maximum possible frictional force (F_max) is given by the coefficient of friction (μ) multiplied by the normal force (N).
- F_max = μ * N
- F_max = 0.4 * 588N
- F_max = 235.2N
Step 4: Determine the magnitude of the frictional force.
- The magnitude of the frictional force (F_friction) is the smaller value between F_max and the horizontal component of the applied force (F_horizontal).
- F_friction = min(F_max, F_horizontal)
- F_friction = min(235.2N, 84.85N)
- F_friction = 84.85N
Therefore, the magnitude of the frictional force between the blocks is 84.85N.