NIMCET 2024 Mathematics PYQ — How much work does it take to slide a crate for a distance of alo… | Mathem Solvex | Mathem Solvex
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NIMCET 2024 — Mathematics PYQ
NIMCET | Mathematics | 2024
How much work does it take to slide a crate for a distance of 25m along a loading dock by pulling on it with a 180N force where the dock is at an angle of 45∘ from the horizontal?
Choose the correct answer:
A.
3.18198×103J
(Correct Answer)
B.
3.18198×102J
C.
3.4341×103J
D.
3.4341×104J
Correct Answer:
3.18198×103J
Explanation
1. Given Data
Magnitude of the pulling force (F) = 180 N
Displacement/Distance (d) = 25 m
Angle between the force direction and the direction of displacement (θ) = 45∘
2. Formula
The work done (W) by a constant force acting at an angle to the displacement is given by the formula:
W=F⋅d⋅cos(θ)
Where:
F is the magnitude of the force applied.
d is the displacement of the object.
θ is the angle between the force vector and the displacement vector.
3. Calculation
Substitute the given values into the formula:
W=180×25×cos(45∘)
We know that cos(45∘)=21≈0.707106:
W=180×25×0.707106
First, multiply the force and displacement numbers:
180×25=4500
Now, multiply by the value of cos(45∘):
W=4500×0.7071068
W≈3181.98 J
4. Scientific Notation Conversion
To express 3181.98 in standard scientific notation, move the decimal point three places to the left:
W=3.18198×103 J
Correct Answer:(A) 3.18198×103 J
Explanation
1. Given Data
Magnitude of the pulling force (F) = 180 N
Displacement/Distance (d) = 25 m
Angle between the force direction and the direction of displacement (θ) = 45∘
2. Formula
The work done (W) by a constant force acting at an angle to the displacement is given by the formula:
W=F⋅d⋅cos(θ)
Where:
F is the magnitude of the force applied.
d is the displacement of the object.
θ is the angle between the force vector and the displacement vector.
3. Calculation
Substitute the given values into the formula:
W=180×25×cos(45∘)
We know that cos(45∘)=21≈0.707106:
W=180×25×0.707106
First, multiply the force and displacement numbers:
180×25=4500
Now, multiply by the value of cos(45∘):
W=4500×0.7071068
W≈3181.98 J
4. Scientific Notation Conversion
To express 3181.98 in standard scientific notation, move the decimal point three places to the left:
