A 58kg skier is coasting down 25degrees slope at an initial velocity of 3,6m per second.A kinetic frictional force of 70N appores the motion.Calculate the net force acting on the skeir, (b)the work done by net force, (c)the final kinetic of the skier using work-energy theorem,(d) the skiers at a point that is displaced 57m downhill
a. Fnet=ma =58×9,8 =569,4
To solve this problem, we'll need to break it down into several steps. Let's calculate each part one by one:
Step 1: Calculate the gravitational force acting on the skier
The gravitational force acting on an object can be calculated using the following formula:
Force (F) = mass (m) x gravitational acceleration (g)
Given:
Mass (m) = 58 kg
Gravitational acceleration (g) = 9.8 m/s² (approximately)
Using the formula above, we can calculate the gravitational force acting on the skier:
F_gravity = 58 kg x 9.8 m/s² = 568.4 N
Step 2: Decompose the gravitational force into its components
As the slope is inclined at an angle of 25°, we need to decompose the gravitational force into its components parallel and perpendicular to the slope.
The component of the gravitational force parallel to the slope is given by:
F_parallel = F_gravity x sin(θ)
θ = 25° (angle of the slope)
F_parallel = 568.4 N x sin(25°) ≈ 241.3 N
Step 3: Calculate the net force acting on the skier
The net force is the difference between the parallel component of the gravitational force and the kinetic frictional force. In this case, we have:
Net Force = F_parallel - Frictional Force
Frictional Force = 70 N (given)
Net Force = 241.3 N - 70 N = 171.3 N
So, the net force acting on the skier is 171.3 N.
Step 4: Calculate the work done by the net force
To calculate the work done by the net force, we can use the formula:
Work (W) = Force (F) x Distance (d) x cos(θ)
Given:
Force (F) = Net Force = 171.3 N (from step 3)
Distance (d) = 57 m (given)
θ = 25° (angle of the slope)
Work (W) = 171.3 N x 57 m x cos(25°) ≈ 7068.34 J
So, the work done by the net force is approximately 7068.34 J.
Step 5: Calculate the final kinetic energy of the skier using the work-energy theorem
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. So, we can use this theorem to calculate the final kinetic energy:
Work (W) = Change in Kinetic Energy
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
Given:
Initial velocity = 3.6 m/s (given)
The initial kinetic energy can be calculated using the formula:
Initial Kinetic Energy = 0.5 x mass x (initial velocity)²
Initial Kinetic Energy = 0.5 x 58 kg x (3.6 m/s)² ≈ 373.248 J
Using the work-energy theorem:
Work (W) = Final Kinetic Energy - Initial Kinetic Energy
7068.34 J = Final Kinetic Energy - 373.248 J
Final Kinetic Energy = 7068.34 J + 373.248 J ≈ 7436.588 J
So, the final kinetic energy of the skier is approximately 7436.588 J.
I hope this helps! Let me know if you have any further questions.
To calculate the net force acting on the skier, we need to first determine the gravitational force and the frictional force.
(a) Gravitational Force:
The gravitational force acting on the skier is given by the formula:
F_gravity = m * g
where
- F_gravity is the gravitational force,
- m is the mass of the skier (58 kg),
- g is the acceleration due to gravity (9.8 m/s^2).
So, F_gravity = 58 kg * 9.8 m/s^2 = 568.4 N.
(b) Net Force:
The net force is the vector sum of all the forces acting on an object. In this case, since the skier is moving in a straight line down the slope, the net force can be calculated as follows:
Net force = F_gravity - Frictional force
Given that the frictional force is 70 N, the net force will be:
Net force = 568.4 N - 70 N = 498.4 N.
(c) Work done by the net force:
Work done by a force can be calculated using the formula:
Work = Force * Distance * cos(theta)
where
- Work is the work done by the force,
- Force is the net force acting on the skier,
- Distance is the displacement of the skier (57m downhill in this case),
- theta is the angle between the force and the direction of displacement. Since the skier is moving downhill, we can consider theta = 0 degrees.
So, Work = 498.4 N * 57 m * cos(0) = 498.4 N * 57 m = 28,416.8 J.
(d) Final kinetic energy of the skier using work-energy theorem:
According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. Therefore, we can calculate the final kinetic energy of the skier using the work done by the net force:
Final Kinetic Energy = Initial Kinetic Energy + Work done
The initial kinetic energy can be calculated using the formula:
Initial Kinetic Energy = 0.5 * m * v^2
where
- m is the mass of the skier (58 kg),
- v is the initial velocity of the skier (3.6 m/s).
So, Initial Kinetic Energy = 0.5 * 58 kg * (3.6 m/s)^2 = 374.4 J.
Therefore,
Final Kinetic Energy = 374.4 J + 28,416.8 J = 28,791.2 J.
Thus, the final kinetic energy of the skier is 28,791.2 J.