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.
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(b) Determine the work done by the normal force exerted by the table.
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(c) Determine the work done by the force of gravity.
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(d) Determine the work done by the net force on the block.
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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?
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To solve these questions, we need to apply some basic principles in physics related to work and energy. Work is defined as the product of force and displacement. The work done by a force can be calculated using the formula W = F * d * cos(θ), where W represents work, F represents force, d represents displacement, and θ represents the angle between the force and displacement vectors.
(a) To find the work done by the applied force, we can use the given values. The force F is given as 10.0 N, and the displacement d is given as 2.40 m. However, we need to calculate the component of the force in the direction of displacement by multiplying the force by the cosine of the angle below the horizontal. The angle is 25.0°, so the component of the force in the direction of displacement is 10.0 N * cos(25.0°). Now we can calculate the work done by the applied force using the formula W = F * d * cos(θ).
(b) The normal force exerted by the table does not do any work since it is perpendicular to the displacement of the block.
(c) The work done by the force of gravity can be calculated using the formula W = m * g * h, where m represents the mass of the object, g represents the acceleration due to gravity (approximately 9.8 m/s²), and h represents the change in height. In this case, there is no change in height, so the work done by the force of gravity is zero.
(d) The work done by the net force on the block can be calculated as the sum of the work done by all the forces acting on the block. In this case, there are only two forces, the applied force and the force of gravity. The net force can be calculated as the vector sum of these forces. Then, using the formula W = F * d * cos(θ), we can calculate the total work done by the net force.
For the second question, we need to apply the concepts of energy conservation and friction. The skier starts with potential energy at the top of the hill, and as the skier glides down the hill, the potential energy is converted to kinetic energy. The kinetic energy is then gradually converted into heat energy by the friction between the skis and the snow. When the skier reaches the horizontal portion of the snow, the frictional force stops the skier. To find the distance the skier glides along the horizontal portion of the snow, 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. We can equate the work done by the frictional force to the change in kinetic energy to find the distance the skier glides.