A luggage handler pulls a 20kg suitcase up a ramp inclined at 25 degrees above the horizontal by a force F of magnigutde 145N that acts parallel to the ramp. The coefficient of kinetic friction between the ramp and the incline is .30. If the suitcase travels 4.6 m along the ramp calculate
a) work done on the suitcase by the force F
b)work done on suitcase by gravitational force.
c) work done on suitcase by normal force
d)work done on suitcase by friciton force
e)total work done on suitcase
f) If the speed of suitcase is zero at bottom of ramp what is its speed after it travels 4.6 m along the ramp?
Are these the correct equations I would use?
a)W=Fd
b)W=mgd cos theda
c)W=Fd cos theda
d) What would be the correct equation for part d)?
And could you help me on part e and f?
a) W = Fd = 145N * 4.6m = 667Nm
b) W = mgd cosθ = 20kg * 9.8m/s^2 * 4.6m * cos25° = 545.2Nm
c) W = Fd cosθ = 145N * 4.6m * cos25° = 471.3Nm
d) W = μFd = 0.3 * 145N * 4.6m = 261.5Nm
e) Total work done on suitcase = W = 667Nm + 545.2Nm + 471.3Nm + 261.5Nm = 2045Nm
f) Speed of suitcase = v = √(2W/m) = √(2 * 2045Nm/20kg) = 10.3m/s
a) The correct equation for work done on the suitcase by the force F is:
W = Fd cosθ
where W is the work done, F is the force parallel to the ramp, d is the distance traveled along the ramp, and θ is the angle of inclination.
b) The correct equation for work done on the suitcase by the gravitational force is:
W = mgd sinθ
where W is the work done, m is the mass of the suitcase, g is the acceleration due to gravity, d is the distance traveled along the ramp, and θ is the angle of inclination.
c) The work done on the suitcase by the normal force is zero since the normal force is perpendicular to the direction of motion.
d) The correct equation for work done on the suitcase by the friction force is:
W = μmgd
where W is the work done, μ is the coefficient of kinetic friction, m is the mass of the suitcase, g is the acceleration due to gravity, and d is the distance traveled along the ramp.
e) To find the total work done on the suitcase, you add the work done by the force F and the work done by the gravitational force:
Total work done = Work done by force F + Work done by gravitational force
f) To determine the speed of the suitcase after traveling 4.6 m along the ramp, you can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy:
Work done = Change in kinetic energy
Using this principle, you can find the final kinetic energy of the suitcase, and then calculate its final speed using the equation:
Kinetic energy = 0.5 * m * v^2
where m is the mass of the suitcase and v is the final speed.
Yes, those equations are correct for parts a, b, and c:
a) W = Fd
b) W = mgd cos(theta)
c) W = Fd cos(theta)
For part d, the work done on the suitcase by the friction force can be calculated using the equation:
d) W = -μN d
where μ is the coefficient of kinetic friction and N is the normal force. The negative sign indicates that the friction force opposes the motion of the suitcase along the ramp.
To solve part e, you need to calculate the individual work done on the suitcase by the different forces and then find the sum:
e) Total work done on the suitcase = Work done by force F + Work done by gravitational force + Work done by normal force + Work done by friction force
To solve part f, you can use the work-energy theorem. The work done on the suitcase will be equal to the change in its kinetic energy. Since the suitcase starts from rest at the top of the ramp, the initial kinetic energy is zero. Therefore:
Total work done on the suitcase = Change in kinetic energy
Using this equation, you can find the speed of the suitcase after it travels 4.6 m along the ramp by calculating the change in kinetic energy and then using the equation:
(1/2)mv^2 = Change in kinetic energy
where m is the mass of the suitcase and v is its final velocity.
Yes, you have the correct equations for parts a, b, and c:
a) The work done on the suitcase by the force F is given by the equation: W = F * d, where W is the work done, F is the magnitude of the force parallel to the ramp, and d is the distance traveled along the ramp.
b) The work done on the suitcase by the gravitational force is given by the equation: W = m * g * d * cos(theta), where m is the mass of the suitcase, g is the acceleration due to gravity (approximately 9.8 m/s^2), d is the distance traveled along the ramp, and theta is the inclination angle of the ramp (25 degrees in this case).
c) The work done on the suitcase by the normal force is zero, because the normal force acts perpendicular to the displacement of the suitcase.
For part d, you need to calculate the work done on the suitcase by the friction force. Since the suitcase is moving, kinetic friction is acting on it. The equation for the work done by friction is: W = f * d, where W is the work done, f is the magnitude of the friction force, and d is the distance traveled along the ramp.
To calculate the friction force, you need to use the equation: f = u * N, where u is the coefficient of kinetic friction and N is the normal force. In this case, since the ramp is inclined, the normal force can be calculated as N = m * g * cos(theta), where m is the mass of the suitcase, g is the acceleration due to gravity, and theta is the inclination angle of the ramp.
Now, let's move on to parts e and f:
e) The total work done on the suitcase is the sum of the work done by all the individual forces acting on it. So, to calculate the total work done, you add the work done by force F, the work done by gravity, and the work done by friction.
f) To calculate the speed of the suitcase after it travels 4.6 m along the ramp, you need to consider energy conservation. When the suitcase reaches the bottom of the ramp, all the potential energy it had at the top is converted into kinetic energy. Therefore, the initial potential energy is equal to the final kinetic energy.
The equation for potential energy is: PE = m * g * h, where PE is the potential energy, m is the mass of the suitcase, g is the acceleration due to gravity, and h is the height of the ramp. Since the suitcase is moving horizontally on the ramp, the height of the ramp does not change. So, you can equate the potential energy at the top of the ramp to the kinetic energy at the bottom of the ramp using the equation: 1/2 * m * v^2 = m * g * h, where v is the final velocity of the suitcase.
To find the final velocity, you can rearrange the equation and solve for v: v = sqrt(2 * g * h), where g is the acceleration due to gravity and h is the height of the ramp.