Question

A student wants to use a ramp to move boxes into a truck bed that is 3 m high. He has a choice of 2 different ramps. The length of one ramp is 4m, and the length of the other ramp is 6m. Which one will make his work easier?

Answer 1

Answer:

the ramp with 6 m length will be easier to work with.

Explanation:

the mechanical advantage of the ramp can be calculated to find out which ramp will be easier to work with. The ramp with greater mechanical advantage will be easier to work with. The formula for the mechanical advantage of ramp is given as follows:

$M.A = \frac{L}{h}$

where,

M.A = Mechanical Advantage = ?

L = Length of Ramp

h = height of ramp = 3 m

FOR L =4 m:

$M.A = \frac{4\ m}{3\ m}\\\\M.A = 1.33$

FOR L = 6 m:

$M.A = \frac{6\ m}{3\ m}\\\\M.A = 2$

Since, the ramp with length 6 m has a greater mechanical advantage.

Therefore, the ramp with 6 m length will be easier to work with.

Answer 2

The second choice ramp with length of 6 m will make his work easier.

The given parameters;

• height of the ramp, h = 3 m
• length of the first ramp = 4 m
• length of the second ramp = 6 m

The mechanical advantage of the each of the choices is calculated as follows;

First choice:

$M.A = \frac{l_1}{h} \\\\M.A = \frac{4}{3} \\\\M.A = 1.333$

Second choice:

$M.A = \frac{l_2}{h} \\\\M.A = \frac{6}{3} \\\\M.A = 2$

Thus, we can conclude that the second choice ramp with length of 6 m will make his work easier.

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