Sure! Let's find the mass of the cart by breaking down the steps:
1. Given values:
- Force applied ([tex]\( F \)[/tex]) = 250 Newtons (N)
- Angle of force ([tex]\( \theta \)[/tex]) = 35 degrees
- Acceleration ([tex]\( a \)[/tex]) = 1.4 meters per second squared ([tex]\( m/s^2 \)[/tex])
2. Resolve the horizontal component of the force:
The force has a vertical and a horizontal component due to the angle. For this problem, we are interested in the horizontal component of the force which contributes to the acceleration of the cart.
The horizontal component ([tex]\( F_{\text{horizontal}} \)[/tex]) of the force can be calculated using the cosine of the angle:
[tex]\[
F_{\text{horizontal}} = F \cdot \cos(\theta)
\][/tex]
Substituting the given values:
[tex]\[
F_{\text{horizontal}} = 250 \cdot \cos(35^{\circ}) \approx 204.788
\][/tex]
3. Use Newton's Second Law to find the mass:
Newton's Second Law states:
[tex]\[
F = ma
\][/tex]
where [tex]\( F \)[/tex] is the net force acting on an object, [tex]\( m \)[/tex] is the mass of the object, and [tex]\( a \)[/tex] is the acceleration.
We can rearrange this formula to solve for the mass ([tex]\( m \)[/tex]):
[tex]\[
m = \frac{F_{\text{horizontal}}}{a}
\][/tex]
Substituting the known values:
[tex]\[
m = \frac{204.788}{1.4} \approx 146.277
\][/tex]
4. Round to the nearest whole number:
[tex]\[
m \approx 146
\][/tex]
Thus, the mass of the cart is [tex]\( 146 \)[/tex] kg. So, to the nearest whole number, the mass of the cart is 146 kg.
