(II) A large crate of mass 1500 kg starts sliding from rest along a frictionless ramp, whose length is ℓ and whose inclination with the horizontal is θ. ( a ) Determine as a function of θ : (i) the acceleration a of the crate as it goes downhill, (ii) the time t to reach the bottom of the incline, (iii) the final velocity v of the crate when it reaches the bottom of the ramp, and (iv) the normal force F N on the crate. ( b ) Now assume ℓ = 100 m. Use a spreadsheet to calculate and graph a , t , v , and F N as functions of θ from θ = 0° to 90° in 1° steps. Are your results consistent with the known result for the limiting cases θ = 0° and θ = 90°?
(II) A large crate of mass 1500 kg starts sliding from rest along a frictionless ramp, whose length is ℓ and whose inclination with the horizontal is θ. ( a ) Determine as a function of θ : (i) the acceleration a of the crate as it goes downhill, (ii) the time t to reach the bottom of the incline, (iii) the final velocity v of the crate when it reaches the bottom of the ramp, and (iv) the normal force F N on the crate. ( b ) Now assume ℓ = 100 m. Use a spreadsheet to calculate and graph a , t , v , and F N as functions of θ from θ = 0° to 90° in 1° steps. Are your results consistent with the known result for the limiting cases θ = 0° and θ = 90°?
(II) A large crate of mass 1500 kg starts sliding from rest along a frictionless ramp, whose length is ℓ and whose inclination with the horizontal is θ. (a) Determine as a function of θ: (i) the acceleration a of the crate as it goes downhill, (ii) the time t to reach the bottom of the incline, (iii) the final velocity v of the crate when it reaches the bottom of the ramp, and (iv) the normal force FN on the crate. (b) Now assume ℓ = 100 m. Use a spreadsheet to calculate and graph a, t, v, and FN as functions of θ from θ = 0° to 90° in 1° steps. Are your results consistent with the known result for the limiting cases θ = 0° and θ = 90°?
A block of mass m slides down from rest on a rough incline of
length 8m where the incline makes an angle of 30° with the
horizontal. The block comes to rest on the rough horizontal surface
after sliding for 4 m. The coefficient of kinetic friction on the
incline is 0.30. The coefficient of kinetic friction on the horizontal
surface is different from the incline, find this value using two approaches:
(i) Using Newton's laws of motion and Kinematics and
30⁰
(ii) Using Work-Kinetic Energy Theorem (Give answer to 2 sig. figs.)
4 m
8 m
WA
A frictionless incline is 5.00 m long (the distance from the top of the incline to the bottom, measured along the incline). The vertical distance from the top of the incline to the bottom is 2.26 m. A small block is released from rest at the top of the incline and slides down the incline.
(i) How long does it take the block to reach the ground?
1) In Figure, a block with mass m = 1 kg is released from height h,
friction until it reaches the path with first length d,= 3 m, where the friction force between B and
C is f, = 9 N, and until it reaches the path, where the friction force between E and F is f, = 7 N.
The height is h, = 1 m, and second horizontal length is d,= 1 m. The block continues its motion
after the point F.
(a) Find the velocity at the point A.
(b) Find the velocity at the point D.
(c) Find the height h if the velocity of m is v= 9 m/s at the point F.(sin45=0.7 g=9.8 m/s²)
11 m. Its path is without
1
m
(F
d,=1 m
h
h, = 11 m
D
45°
E
d,=3 m
h,=1 m
A
В
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