A man with a mass of 100 kg slides down a vertical pole with an acceleration of 8 m/s2. What is the frictional force acting on the man?
since g = -9.8m/s^2, there's a positive acceleration of 1.8m/s^2
F = ma = 100*1.8 = 180N
To find the frictional force acting on the man, we need to consider the forces acting on him while sliding down the pole.
1. Weight (W = m * g): The weight of the man is equal to his mass (m) multiplied by the acceleration due to gravity (g) which is approximately 9.8 m/s^2. Therefore, the weight of the man is W = 100 kg * 9.8 m/s^2 = 980 N.
2. Normal force (N): The normal force is the force exerted by the pole on the man perpendicular to the surface. Since the man is sliding vertically down the pole, the normal force would be equal to the weight of the man (N = W = 980 N).
3. Frictional force (Ff): The frictional force acts parallel to the surface of contact and opposes the motion of the man. Since the man is sliding down the pole with an acceleration of 8 m/s^2, the frictional force can be found using Newton's second law:
Fnet = m * a
Where Fnet is the net force, m is the mass, and a is the acceleration.
Fnet = Ff - W (Since Fnet = Ff - W)
Rearranging the equation:
Ff = Fnet + W
Substituting the given values:
Ff = m * a + W =100 kg * 8 m/s^2 + 980 N = 800 N + 980 N = 1780 N.
Therefore, the frictional force acting on the man is 1780 N.
To find the frictional force acting on the man, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = m * a). In this case, the acceleration is given as 8 m/s^2 and the mass is given as 100 kg.
However, we need to take into account that the man is sliding down a vertical pole, indicating that there is also a gravitational force acting on him. This force can be calculated using the formula F_gravity = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since the man is sliding down, the frictional force must be acting in the opposite direction of the net force. Therefore, the net force can be calculated as the gravitational force minus the frictional force: F_net = F_gravity - F_friction.
Using the formula F = m * a, we can calculate the gravitational force:
F_gravity = m * g
F_gravity = 100 kg * 9.8 m/s^2
F_gravity = 980 N
Now, we can rearrange the equation F_net = F_gravity - F_friction to solve for the frictional force:
F_friction = F_gravity - F_net
Since the acceleration is given as 8 m/s^2, we can calculate the net force using F_net = m * a:
F_net = 100 kg * 8 m/s^2
F_net = 800 N
Substituting the values into the equation, we can solve for the frictional force:
F_friction = 980 N - 800 N
F_friction = 180 N
Therefore, the frictional force acting on the man is 180 N.