A block of mass 2.50 kg is pushed 2.40 m along a frictionless horizontal table by a constant 10.0 N force directed 25.0° below the horizontal.
(a) Determine the work done by the applied force.
J
(b) Determine the work done by the normal force exerted by the table.
J
(c) Determine the work done by the force of gravity.
J
(d) Determine the work done by the net force on the block.
J
2. A skier starts from rest at the top of a hill that is inclined at 9.5° with the horizontal. The hillside is 150 m long, and the coefficient of friction between snow and skis is 0.0750. At the bottom of the hill, the snow is level and the coefficient of friction is unchanged. How far does the skier glide along the horizontal portion of the snow before coming to rest?
m
The only trick here is to break up the force into horizontal components. The pushing force is the horizontal component. I assume you can do that. The vertical component of the pushing force does no work, no does gravity, as there is no movement in the vertical direction.
On the second, I would break it into parts, down the hill, and horizontal.
Potential energy at top of hill=fricion work downhill + friction work horizontal.
PE=mu*mass*g*cosTheta*150 + mu*mass*g*distance.
Notice mass will divide out when you put mgh in for PE, so then solve for distance.
im still really confused
work is done when a force operates in the direction of the force.
work=force*distance, when the force and distance are in the same direction.
To solve these problems, we need to use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
(a) The work done by the applied force can be calculated using the formula:
Work = Force * Distance * cos(theta)
where the force is 10.0 N, the distance is 2.40 m, and theta is 25.0° below the horizontal. We need to find the horizontal component of the force, which is given by:
Force_horizontal = Force * cos(theta)
Plugging in the values:
Force_horizontal = 10.0 N * cos(25.0°)
Now we can calculate the work:
Work = Force_horizontal * Distance
Work = (10.0 N * cos(25.0°)) * 2.40 m
Work = 20.47 J
(b) The normal force exerted by the table does not do any work because the displacement and the force are perpendicular. Therefore, the work done by the normal force is zero.
(c) The work done by the force of gravity can be calculated as:
Work_gravity = Force_gravity * Distance * cos(theta)
where the force of gravity can be calculated using the formula:
Force_gravity = mass * gravity
Given that the mass is 2.50 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the work done by gravity:
Work_gravity = (2.50 kg * 9.8 m/s^2) * 2.40 m * cos(25.0°)
Work_gravity = 49.67 J
(d) The net force is the vector sum of the applied force and the force of gravity. Therefore, the work done by the net force can be calculated as the sum of the works done by the applied force and the force of gravity:
Work_net = Work_applied force + Work_gravity
Work_net = 20.47 J + 49.67 J
Work_net = 70.14 J
2. To determine how far the skier glides along the horizontal portion of the snow before coming to rest, we need to calculate the work done against friction. The work done against friction is equal to the initial kinetic energy of the skier.
The initial kinetic energy can be calculated as:
Initial kinetic energy = 0.5 * mass * velocity^2
Since the skier starts from rest, the initial velocity is zero, so the initial kinetic energy is also zero.
The work done against friction is given by the formula:
Work_friction = Force_friction * Distance
where the force of friction can be calculated using the formula:
Force_friction = coefficient of friction * normal force
The normal force is the weight of the skier, which is given by:
Force_normal = mass * gravity
Plugging in the values:
Force_normal = (mass * gravity) = (mass * 9.8 m/s^2)
Now we can calculate the force of friction:
Force_friction = coefficient of friction * Force_normal
Force_friction = (0.0750) * (mass * 9.8 m/s^2)
The work done against friction is now:
Work_friction = Force_friction * Distance
Work_friction = (0.0750) * (mass * 9.8 m/s^2) * Distance
We need to find the distance, so we rearrange the formula:
Distance = Work_friction / (0.0750 * mass * 9.8 m/s^2)
Since the initial kinetic energy is zero, the work done against friction is also zero. Therefore, the skier glides along the horizontal portion of the snow for a distance of zero meters before coming to rest.