a cart is pulled by a force of 250 n at an angle of 35° above the horizontal. the cart accelerates at 1.4…

a cart is pulled by a force of 250 n at an angle of 35° above the horizontal. the cart accelerates at 1.4 m/s². the free - body diagram shows the forces acting on the cart. the mass of the cart, to the nearest whole number, is kg.

a cart is pulled by a force of 250 n at an angle of 35° above the horizontal. the cart accelerates at 1.4 m/s². the free - body diagram shows the forces acting on the cart. the mass of the cart, to the nearest whole number, is kg.

Answer

Explanation:

Step1: Resolve the pulling - force horizontally

We use the cosine function to find the horizontal component of the pulling force $F_p$. The horizontal component $F_{px}=F_p\cos\theta$, where $F_p = 250$ N and $\theta = 35^{\circ}$. So $F_{px}=250\cos35^{\circ}\approx250\times0.819 = 204.75$ N.

Step2: Apply Newton's second - law

According to Newton's second - law $F = ma$, where $F$ is the net force in the horizontal direction and $a$ is the acceleration. In the horizontal direction, the net force is the horizontal component of the pulling force (assuming no friction), so $F_{px}=ma$. We know $F_{px}\approx204.75$ N and $a = 1.4$ m/s². Then $m=\frac{F_{px}}{a}$.

Step3: Calculate the mass

Substitute the values of $F_{px}$ and $a$ into the formula: $m=\frac{204.75}{1.4}\approx146.25$ kg. Rounding to the nearest whole number, $m = 146$ kg.

Answer:

146