A ramp leading up to a loading platform is 3 m long and 1 m high at its highest point. If the friction is ignored, what work is needed to slide a 600-kg crate up the ramp at a constant speed?
a) 2.00 *10^2 J
b) 5.89 *10^2 J
c) 1.80 *10^3 J
d) 5.88 *10^3 J
I believe the answer is d) but I would just like someone to explain the answer to me and correct me if d) isn't the answer. THANK YOU SO MUCH, in advance :)
Wc = mg = 600kg * 9.8N/kg = 5880 N. =
Wt of crate.
sinA = 1m/3m = 0.3333.
A = 19.47 Deg.
Fc = 5880N @ 19.47 Deg.
Fp = 5880*sin19.47 = 1960 N. = Force
parallel to plane.
W = Fp*d = 1960 * 3 = 5880 Joules.
Well, let me take a shot at explaining the answer to you, but brace yourself for some clowny humor along the way!
To find the work needed to slide the crate up the ramp, we can use the formula for work:
Work = Force x Distance
In this case, the force we need to overcome is the weight of the crate. The weight of an object is given by the formula:
Weight = Mass x Gravity
Since the mass of the crate is 600 kg and the acceleration due to gravity is approximately 9.8 m/s², the weight of the crate is:
Weight = 600 kg x 9.8 m/s² = 5880 N
Now, let's find the distance the crate moves up the ramp. Since the ramp is inclined, we can use trigonometry to determine the distance along the ramp. In this case, we use the hypotenuse of the right triangle formed by the ramp, which is 3 m long, and the height of the ramp, which is 1 m. By using the Pythagorean theorem, we can find the length of the ramp:
Length of ramp = √(3² + 1²) = √10 ≈ 3.16 m
Now that we have the force and distance, we can calculate the work:
Work = Force x Distance
Work = 5880 N x 3.16 m
Work ≈ 18,571.2 J
So, it looks like the correct answer is actually not d), but a clowny-sized c)! The work needed to slide the crate up the ramp at a constant speed is approximately 1.80 * 10³ J.
I hope this clown-centered explanation helps!
To calculate the work needed to slide the crate up the ramp, we need to determine the gravitational potential energy change.
The gravitational potential energy change is given by the formula:
ΔPE = m * g * h
where
m = mass of the crate (600 kg),
g = acceleration due to gravity (9.8 m/s^2), and
h = height of the ramp (1 m).
ΔPE = 600 kg * 9.8 m/s^2 * 1 m
= 5880 J
Therefore, the work needed to slide the crate up the ramp at a constant speed is 5880 J.
Hence, the correct answer is d) 5.88 × 10^3 J.
To find the work needed to slide the crate up the ramp, we can use the formula:
Work = Force x Distance
First, we need to calculate the force. Since the friction is ignored, the only force acting on the crate is its weight. The weight can be calculated using the formula:
Weight = mass x gravity
Given that the mass of the crate is 600 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 600 kg x 9.8 m/s^2 = 5880 N
Next, we need to calculate the distance. The distance is the length of the ramp, which is given as 3 m.
Now, we can calculate the work:
Work = Force x Distance = Weight x Distance
Work = 5880 N x 3 m = 17640 N·m = 17640 J
The work needed to slide the 600 kg crate up the ramp at a constant speed is 17640 J.
Since none of the given options match exactly with the calculated value, we need to round it to the nearest significant figure. Therefore, the closest option is c) 1.80 * 10^3 J.