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Answer:
acceleration = 4.89 m/s²
Explanation:
We can find the acceleration of the mass down the ramp by finding the resultant force.
Refer to the picture, let the x direction parallel to the ramp, then:
[tex]\boxed{\Sigma F_x=w\cdot sin43^o-f}[/tex]
and
[tex]\boxed{\Sigma F_y=N-w\cdot cos43^o}[/tex]
where:
To find the weight (w), we use this formula:
[tex]\boxed{w=mass(m)\times gravity(g)}[/tex]
[tex]\begin{aligned}w&=mg\\&=65.0\times9.8\\&=637\ N\end{aligned}[/tex]
Next, we calculate the normal force using the ΣFy. Since the mass does not move in y direction, then ΣFy = 0.
[tex]\begin{aligned}\Sima F_y&=N-w\cdot cos43^o\\0&=N-637\times cos43^o\\N&=465.9\ N\end{aligned}[/tex]
Then, we can find the friction force by using this formula:
[tex]\boxed{f=coefficient\ of\ friction(\mu)\times normal\ force(N)}[/tex]
[tex]\begin{aligned}f&=\mu N\\&=0.25\times465.9\\&=116.48\ N\end{aligned}[/tex]
Now, we can find the ΣFx.
[tex]\begin{aligned}\Sigma F_x&=w\cdot sin43^o-f\\&=637\times sin43^o-116.48\\&=318.0\ N\end{aligned}[/tex]
By using the Newton's second law, we can find the acceleration:
[tex]\boxed{force(F)=mass(m)\times acceleration(a)}[/tex]
[tex]\begin{aligned}F&=ma\\318.0&=65.0\times a\\a&=\bf4.89\ m/s^2\end{aligned}[/tex]
