Question

a 85 kg runner waits at the starting
line. what force is required reach an
acceleration of 3.4 m/s²?
a 50.5 n force is applied to a golf ball,
generating an initial acceleration of 15
m/s². calculate the mass of the golf
ball.
what would be the acceleration of a
launched projectile from a trebuchet
with a 35 kg mass when the force used
is 1 000 n?
a 0.075 kg bullet travels through the
barrel of a gun, accelerating at 440
000 m/s², before leaving the barrel.
what was the force of launch?
a meteorite accelerates towards a
space station at 0.05 m/s² from an
applied force of 300 n. what is the
mass of the meteorite?
a 0.600 kg dynamics trolley has a 1.5
kg load added. it is launched with a
force of 10 n. what is the
acceleration?

Explanation:

First Problem (85 kg runner, force for 3.4 m/s² acceleration)

Step1: Recall Newton's Second Law ($F = ma$)

Newton's Second Law states that force $F$ is equal to mass $m$ multiplied by acceleration $a$. Here, mass $m = 85\ kg$ and acceleration $a = 3.4\ m/s^2$.

Step2: Calculate the force

Using the formula $F = ma$, substitute the values: $F = 85\ kg\times3.4\ m/s^2$.
$F = 289\ N$

Step1: Recall Newton's Second Law ($F = ma$), rearrange for mass

We know $F = ma$, so to find mass $m$, we rearrange the formula to $m=\frac{F}{a}$. Here, $F = 50.5\ N$ and $a = 15\ m/s^2$.

Step2: Calculate the mass

Substitute the values into the formula: $m=\frac{50.5\ N}{15\ m/s^2}\approx3.37\ kg$ (rounded to two decimal places)

Step1: Recall Newton's Second Law ($F = ma$), rearrange for acceleration

From $F = ma$, we get $a=\frac{F}{m}$. Here, $F = 1000\ N$ and $m = 35\ kg$.

Step2: Calculate the acceleration

Substitute the values: $a=\frac{1000\ N}{35\ kg}\approx28.57\ m/s^2$ (rounded to two decimal places)

Answer:

The required force is $289\ N$.

Second Problem (50.5 N force, 15 m/s² acceleration, find golf ball mass)