A constant frictional force of 32N acts on block of mass m.Calculate the magnitude of the angle theta that will keep the system moving at constant velocity.
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normal force = m g - T sin A if pull force T is up at angle A
friction force = mu ( m g - Tsin A)
if no acceleration then T cos A = friction force = mu(mg-T sinA)
and friction force, mu(mg-Tsin A) = 32
T cos A = 32 = mu m g - mu T sin A
T (cos A + mu sin A) = mu m g
it would be helpful to know mu and m
To calculate the magnitude of the angle theta that will keep the system moving at a constant velocity, we need to consider the forces acting on the block.
The force of gravity acting on the block can be calculated using the formula:
F_gravity = mass * acceleration_due_to_gravity
where acceleration_due_to_gravity is approximately equal to 9.8 m/s^2.
F_gravity = m * 9.8
The component of the force of gravity that acts in the opposite direction of motion is given by:
F_gravity_parallel = F_gravity * sin(theta)
The frictional force acting on the block is given as 32 N. Since the system is moving at a constant velocity, the frictional force must be equal to the parallel component of the force of gravity:
F_gravity_parallel = 32 N
Therefore,
m * 9.8 * sin(theta) = 32
To find the value of theta, we can rearrange the equation:
sin(theta) = 32 / (m * 9.8)
Now, we can solve for theta:
theta = sin^(-1)(32 / (m * 9.8))
This formula will give you the magnitude of the angle theta that will keep the system moving at a constant velocity.