Answer:
a) We can use the following formula to calculate the acceleration of the object:
a = (v_f - v_i) / t
where a is the acceleration, v_f is the final velocity, v_i is the initial velocity, and t is the time interval. Substituting the given values, we get:
a = (90 m/s - 40 m/s) / (2 min * 60 s/min) = 0.83 m/s^2
The force applied causing it to speed up can be found using Newton's second law of motion:
F = m * a
where F is the net force, m is the mass of the object, and a is the acceleration. Substituting the given values, we get:
F = 0.05 kg * 0.83 m/s^2 = 0.042 N
Therefore, the force applied causing the object to speed up is 0.042 N.
b) The work done by this force can be calculated using the following formula:
W = F * d
where W is the work done, F is the net force, and d is the displacement of the object. The displacement of the object is given by:
d = 670 m
Substituting the given values, we get:
W = 0.042 N * 670 m = 28.14 J
Therefore, the work done by the force is 28.14 J.
c) The work done by friction can be calculated using the formula:
W_friction = F_friction * d
where W_friction is the work done by friction, F_friction is the force of friction, and d is the displacement of the object. The force of friction can be calculated using:
F_friction = μ * F_norm
where μ is the coefficient of friction and F_norm is the normal force. The normal force is equal to the weight of the object, which is given by:
F_weight = m * g
where m is the mass of the object and g is the acceleration due to gravity. Substituting the given values, we get:
F_weight = 0.05 kg * 9.81 m/s^2 = 0.49 N
The normal force is equal in magnitude to the weight of the object, so we have:
F_norm = F_weight = 0.49 N
Substituting the given coefficient of friction, we get:
F_friction = 0.34 * 0.49 N = 0.17 N
The work done by friction can now be calculated by substituting the values we have found:
W_friction = 0.17 N * 670 m = 113.9 J
Therefore, the work done by friction is 113.9 J.
d) The net work done can be calculated as the sum of the work done by the applied force and the work done by friction:
W_net = W_applied + W_friction
Substituting the values we have found, we get:
W_net = 28.14 J + 113.9 J = 142.0 J
Therefore, the net work done is 142.0 J.