1.)A force of 250 is just sufficient to start a 50 kg steel trunk moving across a wooden floor. Find the coefficient of static friction.
2.) compute the acceleration of the block sliding down a 30 deg inclined plane if the coefficient of kinetic friction is 0.20.
force friction=mg*mu
mu=250N/(50*9.8)
2. gravity force down the plane
mg*sin30
net force=m*acceleration
mg*sin30-mg*.2=ma
solve for acceleration a
Thank you :)
To find the coefficient of static friction in question 1, we can use the formula:
μs = Fs / N
where μs is the coefficient of static friction, Fs is the static friction force, and N is the normal force.
In this case, the force required to start the trunk moving is the static friction force. Given that the force is 250 N, we can substitute Fs = 250 N and solve for N.
N is the normal force acting on the trunk, which is equal to the weight of the trunk. Weight is calculated by multiplying the mass (50 kg) by the acceleration due to gravity (9.8 m/s^2). Therefore, N = 50 kg * 9.8 m/s^2.
Substituting these values into the formula, we get:
μs = 250 N / (50 kg * 9.8 m/s^2)
Calculating this expression will give us the coefficient of static friction.
For question 2, to compute the acceleration of the block sliding down the inclined plane, we need to consider the forces acting on the block. These forces are gravity, the normal force, and the frictional force.
The net force acting on the block is given by:
Fnet = m * a
where Fnet is the net force, m is the mass of the block, and a is the acceleration.
The weight of the block (force due to gravity) can be calculated as:
W = m * g
where W is the weight, m is the mass, and g is the acceleration due to gravity (9.8 m/s^2). The component of the weight acting parallel to the inclined plane is:
W_parallel = W * sin(theta)
where theta is the angle of the inclined plane (30 degrees in this case). The normal force is the component of the weight acting perpendicular to the inclined plane:
N = W * cos(theta)
The frictional force can be calculated as:
F_friction = μk * N
where μk is the coefficient of kinetic friction and N is the normal force.
The net force is equal to the component of the weight parallel to the plane minus the force of friction:
F_net = W_parallel - F_friction
Substituting the formulas and values into the equation F_net = m * a, we can solve for the acceleration a.
Note that since the block is sliding, we use the coefficient of kinetic friction in this case.